Question: Rewrite as a simplified fraction. ${3.5\overline{23} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3523.2323...\\ 10x &= 35.2323...\end{align*}}$ Subtracting the two equations, we have: ${990x = 3488}$ ${x = \dfrac{3488}{990}} $ ${x = \dfrac{1744}{495}} \text{or} {3 \dfrac{259}{495}}$